How to prevent the "Minmus Quake" that is destroying my base

Have you tried Kerbal Joint Reinforcement. That usually fixes shaking and wobbling glitches. Kerbal Joint Reinforcement

If you're using KAS and KIS, you can keep the base from jumping (although not breaking apart at seams if the 'quake' is serious by application of the Launch Clamps AKA Launch Stability Enhancers.

It's not easy - the largest KIS container can only fit one launch clamp, and they are extremely ungrateful once 'out in the open' - soon after 'deployment' (switching craft/kerbal' or such) they 'solidify' and become absolutely 100% immovable - there is no force in the world that can move a 'solidified' launch clamp, and while the joint to whatever it attaches to is subject to normal physics rules, it's very, very sturdy.

Note: attach the clamps into 'one smooth motion' - straight from the inventory to the attach location. Don't drop them along the way, don't attach them to other parts, and above all do NOT try to change the attachment point of an already solidified clamp, or rotate it. The clamp won't move. But the attachment point WILL change. So your base will 'move' to adapt. Usually in a rather explosive manner.

Extra benefit: the clamps generate 25% more power than the RTG at maybe 5% the price.